Hope this is the right place. Just purchased an old Ideal ship model. Parts are printed on thin wood - similar to old balsa airplane kits. When building airplanesfor me in the 50’s my dad used to soak the sheets in water to keep them from cracking/splitting when cut from the sheet.
Great idea to scan them first. For printed parts I don’t use blades to cut them really close to the line, I use an Xacto chisel blade or anything similar and very sharp, then I use that to cut the parts out and leave about 1/4 inch of material outside the print line. Chiseling straight down on the wood avoids splitting by slicing, slicing leaves you working with the grain of the wood.
When parts are free, then I use sanding sticks to sand away excess material and work my way to the print line. It goes rather quickly and preserves the strength of the wood, splits in the wood can work against you.
First question is- will the result be a flying model? If so, weight is an issue, so that affects the result. I second the suggestion to scan the parts first.
Second, I prefer white glue for working on balsa kits.
Now, on ways to do it. Using a water-based glue for stiffening wood is that this will induce warping and curling if you wet the whole part. So you need prevent warping. Lay a sheet of thin plastic (food wrapping stuff) on a flat surface, then lay the parts on the plastic. Soak parts in a mix of about 1:1 glue/water mix. Then place another sheet of plastic on top, and then place a book on top of the last sheet of plastic.
If weight is not an issue, you can glue a sheet of paper on top and bottom, again with sheet of plastic top and bottom to prevent warping. This will make very strong parts
Another way is to transfer scanned image to plastic either with toner transfer paper requires laser printer. Depending on size/scale of model, I’d suggest 0.030 styrene, thinner for small scale, thicker for large model.
Then, for gluing these parts together I’d use gel CA.
I have strenthened balsa parts, both sides, with a little thin CA. Again thin plastic on both sides and weighted with book- the parts will warp or curl like crazy.
I used to have a 50 year old table jigsaw that used a thin coping saw blade, under tension. ( A very dangerous thing!) It did a great job of cutting out those printed sheet balsa parts. I don’t know if such a thing is available today. It worked like a vibrator, moving the blade up and down, very noisy, with no safety guard of any sort. Luckily, I never injured myself.
For glue, I used good old fashioned airplane glue, the kind with the smell that can get you “high”, another vestage of the olden days!